I am currently trying to make a side scroller beat em up with the ability to move up and down in a plane as well as jumping (kinda like castle crashers)

You could do it either way. Which way you want to do it is going to depend on you.

If you do it in '2D', you just move the player up and down the y axis to simulate moving in and out on the z axis.  Then you render based on their y axis position, bottom to top, to simulate that objects are in front or behind others.  Jumping is a special case here, because instead of using the y axis to simulate z, you actually want to move them along the y axis temporarily.  You would keep track of their state, and if jumping, rendering them on their 'real' z plane.

For collision detection with this method I would assume your z plane would be chunked up a bit, imagine highway lanes, and anything in a lane is collidable with other things in that lane.

I would personally go with Vector3's. If it is essentially a 2D game, having the Z component doesn't complicate things much at all - and it allows you to keep the integrity of the X and Y components.

But it's probably just personal preference. You could prototype both Vector2's and Vector3's and see which you are more comfortable with.